If you are using Internet Explorer 10
(or later), you might find some of the links I have used won't work properly
unless you switch to 'Compatibility View' (in the Tools Menu); for IE11 select
'Compatibility View Settings' and then add this site (anti-dialectics.co.uk). I have as yet no idea how
Microsoft's new browser,
Edge, will handle these links.

~~~~~~oOo~~~~~~

As is the case with all my
work, nothing here should be read as an attack
either on Historical Materialism [HM] -- a theory I fully accept --, or,
indeed,
on revolutionary socialism. I remain as committed to the self-emancipation of the
working class and the dictatorship of the proletariat as I was when I first became a revolutionary
nearly thirty years ago.

The
difference between
Dialectical Materialism [DM] and HM, as I see it, is explained
here.

~~~~~~oOo~~~~~~

This is an Introductory Essay,
which has been written for those who find the
main Essays either too long, or too difficult. It doesn't pretend to be comprehensive
since it is simply a summary of the core ideas presented at this site. Most of the
supporting evidence and argument found in each of the main Essays has been
omitted. Anyone wanting more details, or who would like to examine my arguments
in full, should consult the Essay for which this is a summary. [In this
particular case, that can be foundhere.]

Phrases like "ruling-class theory", "ruling-class view of reality",
"ruling-class ideology" (etc.) used at this site (in connection with
Traditional Philosophy and DM), aren't meant to
suggest that all or even most members of various ruling-classes
actually invented these ways of thinking or of
seeing the world (although some of them did -- for example,
Heraclitus,
Plato,
Cicero,and
Marcus Aurelius).
They are intended to
highlight theories (or "ruling ideas") that are conducive to, or which rationalise the
interests of the various ruling-classes history has inflicted on humanity, whoever invents them.
Up until
recently this dogmatic approach to knowledge had almost invariably been promoted by thinkers who
either relied on ruling-class patronage, or who, in one capacity or another, helped run
the system
for the elite.**

However, that will become the
central topic of Parts Two and Three of Essay Twelve (when they are published); until then, the reader is
directed
here,
here, and
here for
more
details.

[**Exactly
how this applies to DM will, of course, be explained in the other Essays
published at this site (especially
here,
here,
and here).
In addition to the three links in the previous paragraph, I have summarised the
argument (but this time aimed at absolute beginners!)
here.]

Anyone using these links must remember that
they will be skipping past supporting argument and evidence set out in earlier
sections.

If your Firewall/Browser has a pop-up blocker, you will need to press the
"Ctrl" key at the same time or these and the other links here won't work!

I have adjusted the
font size used at this site to ensure that even those with impaired
vision can read what I have to say. However, if the text is either too
big or too small for you, please adjust your browser settings!

In Essay Five I have set out to demolish Engels's
surprisingly brief, but no less superficial,
'analysis' of motion:

"[A]s soon as we consider
things in their motion, their change, their life, their reciprocal
influence…[t]hen we immediately become involved in contradictions. Motion itself
is a contradiction; even simple mechanical change of place can only come about
through a body being both in one place and in another place at one and the same
moment of time, being in one and the same place and also not in it. And the
continual assertion and simultaneous solution of this contradiction is precisely
what motion is." [Engels (1976), p.152.]

This is, of course, an idea Engels appropriated from
Hegel, who in turn derived it from a paradox
invented by
Zeno (490?-430?BC), an ancient Idealist and
Mystic who concluded that motion was impossible (by just thinking about it!).

There are several serious problems with the
above passage, difficulties
that need addressing even before its fatal weaknesses are highlighted.

1) The first of these is connected with
Engels's claim that the alleged 'contradiction' here has something to do with
its "assertion" and "solution". This isn't easy to square with his other stated belief that matter is
independent of mind. Who, for example, "asserted" this alleged contradiction
before humanity evolved? And who did the
"solving"?

Or, are we to assume that things only began
to move when sentient beings capable of making assertions appeared on the scene?

2) The next difficulty centres around the
question whether this alleged 'contradiction' can in fact explain motion. No
one imagines (it is to be hoped!) that this 'contradiction' works like a sort of
'internal metaphysical motor', powering objects along. But, as we will see in
Essay Eight Part One, this is
precisely what dialecticians like Lenin appeared to think:

"The
identity of opposites…is the recognition…of the contradictory, mutually
exclusive, opposite tendencies in all phenomena and processes of
nature…. The condition for the knowledge of all processes of the world in their
'self-movement', in their spontaneous development, in their real life, is the
knowledge of them as a unity of opposites. Development is the 'struggle' of
opposites. The two basic (or two possible? or two historically observable?)
conceptions of development (evolution) are: development as decrease and increase,
as repetition, and development as a unity of opposites (the division of a
unity into mutually exclusive opposites and their reciprocal relation).

"In the first conception of
motion, self-movement, its driving force, its source, its motive,
remains in the shade (or this source is made external -- God, subject,
etc.). In the second conception the chief attention is directed precisely to
knowledge of the source of 'self-movement'.

"The first conception is lifeless,
pale and dry. The second is living. The second alone furnishes the key to the 'self-movement' of everything
existing; it alone furnishes the key to the 'leaps,' to the 'break in
continuity,' to the 'transformation into the opposite,' to the destruction of
the old and the emergence of the new.

"The
unity (coincidence, identity, equal action) of opposites is conditional, temporary, transitory, relative. The
struggle of mutually exclusive opposites is absolute, just as development and
motion are absolute." [Lenin (1961), pp.357-58. Italic emphases in
the original. Bold emphases added.]

It could be argued that this is a little too
glib. Maybe so, but that particular reaction will be tested to destruction in Essay Eight
Part One.

Independently of that, it isn't easy to see
how an object being in one place and not in it, as well as being in two places at once,
can explain how or why it actually moves. At best, this alleged
'contradiction' is derivative -- that is, it is reasonably clear that it is motion
that explains (or which initiates) the 'contradiction', not the other way round. But, if
that is so,
what explains motion?

Plainly, if dialecticians want to cling on to
this 'theory', they will find they can't actually explain why objects move, which is
rather odd since they spare no opportunity regaling us with the claim
thatthey are the only ones who can!

[DM = Dialectical
Materialism.]

It could be objected that DM-theorists in
fact appeal to contradictory forces to account for motion, but we will
see in Essay Eight Part Two that
there is no interpretation that can be placed on the word "force", or on the
word "contradiction", that will sustain such an archaic,
animistic view of change and
movement.

["Archaic" in the sense that it was an early
Greek idea that moving objects needed something to sustain their motion.
In contrast, modern Physics merely deals with change in
motion/momentum, and, in order to do that, most theorists have dropped all
reference to forces. Details can be found in Essay Eight Part Two,
here.
"Animistic" since this idea also depends on another ancient dogma that
conflict and motion can only be explained in terms of the 'will' of some 'god', or as the result of an 'animating spirit' of some
description.]

But, even if forces were 'contradictory',
and reference to a continual cause of motion was both available and
acceptable to modern physics, that would hardly explain how an object being in
one place and not in it, occupying in two places at once, could actually explain why it moves. Plainly,
this alleged 'contradiction' does no work.

Moreover, even in DM-terms, this fable makes
little sense. Are we really supposed to believe that an object that is 'here' is
made to move by its being 'not here' --, its 'dialectical' opposite, its
'other' (as Hegel and Lenin called them)?
Or, that the two 'places' mentioned are locked in some sort of 'struggle', as
the
DM-classicists claim is the case with
all such 'dialectical' opposites? Or even that
the one turns into the other -- i.e., that 'here' turns into 'not here', and
'not here' turns into 'here' --, as the aforementioned DM-worthies also
asserted?

3) Engels's 'analysis' was itself based
on a very brief and sketchy thought experiment
(Hegel's and Zeno's were based on similar word juggling), one
that was in turn motivated by a superficial
consideration of a limited range of terms associated with this phenomenon.

Despite this,
Engels was quite happy to derive a set of universal truths about motion --
applicable everywhere in the entire universe, for all of time -- from the alleged
meaning of a few simple expressions. Clearly, the concepts Engels used cannot have been
derived by 'abstraction' from his (or from anyone else's) experience of moving
bodies, since no conceivable experience could confirm that a moving body is in two
places at once, only that it moves between at least two locations in a finite
interval of time.

To be sure, that is why Engels not only had to indulge in flights-of-fancy to make his case, it is also why he had to impose his views on reality. This was despite his promise that it was something
he would never do:

"Finally, for me there could be no question of
superimposing the laws of dialectics on nature...." [Engels
(1976), p.13. Bold emphasis added.]

In which case, the following characterisation of
Idealism clearly applies to Engels's 'analysis' of motion:

"A consistent
materialism can't proceed from principles which are validated by appeal to
abstract reason, intuition, self-evidence or some other subjective or purely
theoretical source. Idealisms may do this. But the materialist philosophy
has to be based upon evidence taken from objective material sources and verified
by demonstration in practice...." [Novack
(1965), p.17. Bold emphasis added.]

But, this is precisely what Zeno and Hegel did, just
as it accurately describes Engels's approach; all three "proceed[ed] from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source."

4) Putting this to one side, even if Engels's
claims were correct, they couldn't account for movement (and hence they
can't explain change), anyway. Clearly, Engels failed to notice (just as
subsequent dialecticians have also failed to notice)
that the way he depicts motion doesn't distinguish moving from stationary bodies.
Stationary bodies can be in two places at once, and they can be in one place and
not in it at the same time. For example, a car can be in a garage and not
in it at the same moment (having been left parked half-in, half-out); and it can
be in two places at once (in the garage and in the yard), and stationary with
respect to some
inertial frame, all the while.
[Several obvious and less obvious objections to this argument have been
neutralised in
Essay Five.]

Exception could be taken to the above in that it
implicitly uses, or it implies the use of, phrases like "not wholly in one
place" (i.e., the car in question was "half-in, half-out" of the garage). It
could be argued that Engels was quite clear about what he meant: motion involves
a body being in one place and in another at the same time, being in and not in
it at one and the same moment. There is no mention of "not wholly in" in what
Engels asserted.

Or, so it could be maintained.

Clearly, this objection depends for its force on what Engels actually intended
by the following words:

"[E]ven simple mechanical change of place can only
come about through a body at one and the same moment of time being both in one
place and in another place, being in one and the same place and also not in it."
[Loc cit.]

Here, the problem centres on the word "in". Again,
it could be objected that "in" has been illegitimately replaced by "(not)
totally or wholly in", or its equivalent. Even so, it is worth noting that
Engels's actual words imply that this is a legitimate, possible interpretation
of what he said (paraphrased below):

M1: Motion involves a body being in one and the same place and not in it.

If a body is "in...and not in" a certain place it can't in fact be
totally in that place. So, Engels's own words allow for his "in" to
mean "not wholly in", or something like it.

A mundane example of this might be where, say, a 15 cm long pencil is sitting in
a pocket that is only 10 cm deep, while the jacket itself is in a wardrobe. In
that case, it would be perfectly natural to say that this pencil is in, but not
entirely in, the pocket -- that is, it would be both "in and not in" the
pocket at the same time, and in two places at once (in the pocket and in the
wardrobe -- thus fulfilling Engels's definition) --, but still at rest with
respect to some inertial frame. M1 certainly allows for such a situation,
and Engels's use of the word "in" and the rest of what he said plainly carry
this interpretation.

The only way this and other
counter-examples can be neutralised by DM-fans is to re-define the relevant terms in
a way
that would in the end make Engels's 'analysis' inapplicable to material bodies.
It would do this by applying it solely to immaterial, mathematical points
-- plainly
because only a stationary mathematical point can be in precisely one point at any
one time. Unfortunately,
in that case, Engels's thought experiment would no longer apply to what is
supposed to be unique
to movingmaterialobjects.

Either way, unless augmented in some way, Engels's words cannot be used to
distinguish moving from stationary bodies. In which case, it is now quite clear
that this apparent 'contradiction' has arisen simply because of the ambiguities
inherent in the language Engels used -- since, once more, his 'analysis' can't
actually distinguish moving from stationary bodies. When these ambiguities have
been removed (as they have been in Essay
Five), the 'contradiction' simply disappears; no one supposes cars and/or
pencils are contradictory for simply remaining stationary. The same is the case
with moving bodies.

Anyway, mathematical points themselves
cannot move. If they could they would have to occupy still other points.
But points aren't containers (they have no shape, circumference or volume,
otherwise they wouldn't be points -- they have no physical dimensions or
rigidity, so they can't even 'push' each other out of the way as they 'try' to
'move'), so nothing can occupy them. In that case once more, such points
can't
move.

[Certainly, there are mathematicians who talk as if they believe points can
move, but, beyond a certain way of speaking (i.e., figuratively), there
is nothing to support the idea that they can move (and everything to suggest they can't -- not the
least of which is that such points do not exist in space and time to be able
to move anywhere).
On this, see Essay Seven Part One,
here. Indeed, if
certain ways of speaking
could make things move,
far more of us would believe in magic.]

Alternatively, anyone who claimed
that mathematical points could move would have a hard time explaining where they
moved to, where they were before they moved, and how they could be
contradictory -- indeed, if these points were only the same size as any point they
allegedly 'occupied', it would mean they could not be in two such
places at once, or they would have expanded. [That is, one point would
now be two points!] Moreover, such an 'explanation' would
have to be given without an appeal to yet another set of
mathematical points for them to 'occupy', shifting this problem to the next stage.

5) Engels's claim that motion is
contradictory only follows if a body cannot logically be in two places at once,
or if it cannot be in one place and not in it at the same time. Engels just
assumed the truth of this premiss; he nowhere tried to justify it (and no
one since seems to have bothered to do so, either).

[Some might point to
Graham
Priest's work in this area, but it is far from clear that his 'contradictions'
are 'dialectical' to begin with, or even that his analysis makes sense. On that,
see here.]

However, because an ordinary stationary
material body can be in two places at once, and in one place and not in it at
the same time (as we have already seen), Engels's key premiss is not even empirically
true! In that case, it certainly can't be a logical/conceptual truth restricted only to
moving bodies. If it is true that stationary objects can also do what Engels
says, then it cannot be a contradiction when moving bodies do it, too -- or, at
least, it can't
be a contradiction true only of moving bodies. In that case, it cannot be
something that accounts for motion or even distinguishes it from rest.

Of course, it could be argued that the
'contradictions' Engels was interested in are 'dialectical contradictions', not
logical contradictions. However, his wording doesn't support such an
interpretation:

"Motion itself is a
contradiction; even simple mechanical change of place can only come about
through a body being both in one place and in another place at one and the same
moment of time, being in one and the same place and also not in it. And the
continual assertion and simultaneous solution of this contradiction is precisely
what motion is." [Engels (1976), p.152.]

It certainly seems from this that Engels was
talking about logical contradictions as much as about 'dialectical
contradictions'.

And, believe it or not, that would in fact
prove to be good
news for DM-fans, for we have at least got some sort of handle on logical
contradictions. The other sort (i.e., 'dialectical contradiction') has resisted
all attempts at explanation for nigh on 200 years (not that anyone has been
trying all that hard). [In fact, the best Marxist attempt to do this (to date) has been demolished
here.]

6) Furthermore, there are serious problems connected
with what Engels did say: that a moving object is "in one and the same
place and also not in it". But, if moving object, B, isn't located
at, say, X (i.e., if it is "not in X"), then it can't also
be located at X (since it is "not in X", i.e., it isn't there!)
contrary to what Engels asserted. If it isn't there then isn't there. On
the other hand, if Bis located at X, then it can't also
not be at X. Otherwise, Engels's can't mean by "not" what the rest of
us mean by that word.

But, what did he mean?

Unfortunately, he neglected to say, and no DM-fan since has been any clearer.
Other than holding up their hands and declaring it a 'contradiction', there is
nothing more they could say. Once more, this can only mean that they,
too, mean something different by "not" -- for example, for them "is not" seems
to mean "is and is not"! If so, they certainly can't respond by saying "This is
not what we mean", since this use of "not" implies they really mean "This is and
is not what we mean" (as each "is not" is replaced by its 'dialectical
equivalent', "is and is not"), and so on.

As we can see, anyone who falls for Zeno, Hegel or Engels's linguistic conjuring
trick can't actually tell us what they do mean!

Nor can it be replied that Engels's words only apply to movement and change,
hence if or when dialecticians use "is not" -- as in, for example, "This is not
what we mean" -- they don't also mean "This is and is not what we mean". That is
because, if everything is constantly changing into what it is not (as
DM-theorists maintain) then so are the words they use. Hence, "This is what we
mean" must have changed into "This is and is not what we mean".

[The "relative stability defence" has been neutralised in Essay Six,
here and
here.]

7) More specifically, in relation to moving bodies,
it is pertinent to ask the following question: How far apart are the two
proposed "places" that a moving object is supposed to occupy while at the same
time not occupying one of them? Is there a minimum distance involved? The
answer can't be "It doesn't matter; any distance will do." That is
because, as we will see, if a moving object is in two places at once,
then it can't truly be said to be in the first of these before it is in
the second (since it is in both at the same time!). So, unless great care
is taken specifying how far apart these "two places" are, this view of motion
would imply that, say, an aeroplane must land at the same time as it took off!
If any distance will do, then the distance between the two
airports involved is as good as any. [I will return to this topic below.]

So, indifference here would have you arriving at your destination at the same
time as you left home!

Hence, if object B is in one place and then in another (which is,
I suspect, central to any notion of movement that Engels would have accepted),
it must be in the first place before it is in the second. If so, then
time must have elapsed between its occupancy of those two locations, otherwise
we wouldn't be able to say it was in the first place before it was in the
second. But, if we can't say this (that is, if we can't say that it was
in the first place before it was in the second), then that would
undermine the assertion that B was in fact moving, and that it had
travelled from the first location to the second.

Hence, if B is in both locations at once, it can't have moved
from the first to the second. On the other hand, if B has
moved from the first to the second, so that it was in the first before
it reached the second, it can't have been in both at the same time.

If DM-theorists don't mean this, then they must either (i) Refrain from using
"before" and "after" in relation to moving objects, or (ii) Explain what they
do mean by any of the words they use. Option (i) would prevent them from
explaining (or even talking about!) motion.

We are still waiting for them to respond to (or even acknowledge) option
(ii).

Anyway, whatever the answer to these annoying conundrums happens to be -- as is
well known -- between any two locations there is a potentially infinite number
of intermediary points (that is, unless we are prepared to impose an a priori
limitation on nature by denying this).

Does a moving body, therefore, (a) occupy all of these intermediate points at
once? Or, (b) does it occupy each of them successively?

If (a) is the case, does this imply that a moving object can be in an
infinite number of places at the same time, and not just in two, as
Engels asserted?

On the other hand, if Engels is correct, and a moving body only occupies
at most two places at once, wouldn't that suggest that motion is
discontinuous? That is because, such an account seems to picture motion as a
peculiar stop-go sort of affair, since a moving body would have to skip past --
but not occupy, somehow? -- the potentially infinite number of
intermediary locations between any two arbitrary points (the second of which it
then occupies). This must be so if it is restricted to being in at most two
of them at any one time, and is therefore stationary at the second of these
two points.

That is what the "at most" qualifier here implies.

But, that itself appears to run contrary to the hypothesis that motion is
continuous and therefore 'contradictory' --, or, it runs counter to that
hypothesis in any straight-forward sense, at the very least. It is surely the
continuous nature of motion that poses problems for a logic (i.e., Formal Logic
[FL]) which is allegedly built on a static, discontinuous view of
reality, this being the picture that traditional logic is supposed to have
painted --, or, so we
have been told by dialecticians.

It could be argued that no matter how much we 'magnify' the path of a moving
body, it will still occupy two points at once, being in one of them and not in
it at the same time. And yet, that doesn't solve the problem, for if there is
indeed a potentially infinite number of intermediary points between any two
locations, a moving body must occupy more than two of them at once,
contrary to what Engels seems to be saying:

"[A]s soon as we consider things in their motion,
their change, their life, their reciprocal influence…[t]hen we immediately
become involved in contradictions. Motion itself is a contradiction; even simple
mechanical change of place can only come about through a body being both in
one place and in another place at one and the same moment of time, being in one
and the same place and also not in it. And the continual assertion and
simultaneous solution of this contradiction is precisely what motion is." [Loc
cit. Bold emphasis added.]

Hence, between any two points, P and Q
-- located at, say, (X(P), Y(P), Z(P))
and (X(Q), Y(Q), Z(Q)),
respectively -- that a moving object, B, occupies (at the same "moment in
time", T(1)), there are, for example, the following intermediary
points: (X(1), Y(1), Z(1)), (X(2),
Y(2), Z(2)), (X(3), Y(3),
Z(3)),..., (X(i), Y(i), Z(i)),...,
(X(n), Y(n), Z(n)) -- where n
itself can be arbitrarily large. Moreover, the same applies to (X(1),
Y(1), Z(1)) and (X(2), Y(2),
Z(2)): there is a potentially infinite number of intermediate
points between these two, and so on.

So, if Engels is right, B must occupy not just P and Q at
the same instant, it must occupy all these intermediary points, as well --
again, all at T(1). That can only mean that B is located in
a potentially infinite number of places, all at the same "moment". It must
therefore not only be in and not inP at T(1), it
must be in and not in each of (X(1), Y(1), Z(1)),
(X(2), Y(2), Z(2)), (X(3),
Y(3), Z(3)),..., (X(i), Y(i),
Z(i)),..., (X(n), Y(n), Z(n))
at T(1), just as it must also be in all the intermediary points
between (X(1), Y(1), Z(1)) and (X(2),
Y(2), Z(2)), if it is also to be in Q at the
same "moment".

And, what is worse: B must move through (or be in) all these
intermediate points without time having advanced one instant!

That is, B will have achieved all this in zero seconds!

B must therefore be moving with an infinite velocity between P
and Q!

Of course, we could always claim that by "same moment" Engels meant "same
temporal interval", but this scuppers his 'theory' even faster. That is because
if by "same moment" Engels meant "same temporal interval", then there is no
reason why "same point" can't also mean "same spatial interval", at which point
the alleged 'contradiction' simply vanishes (no pun intended).

However, if B moves from P to Q
in temporal interval, T, comprised of sub-intervals, T(1),
T(2), T(3), ..., T(n), each of which
is also comprised of its own sub-intervals, then B will be located at
P at T(1) and then at Q at T(n), which
will, of course, mean that B won't be in these two places at the same
time, although it will be located at these two points in the same
temporal interval. Once again, the 'contradiction' Engels claims to see here
would in that case have vanished. Few theorists, if any, think it is the least
bit contradictory to suppose that B is in P at one moment and then
in Qa moment later.

Consider a car travelling north across Texas during a three-hour temporal
interval. Let us suppose it is in the centre of
Lubbock
at 08:00am and in the centre of
Amarillo
(approximately 124 miles away) at 11:00am. In that case, it will have been in
two locations during the same temporal interval (lasting three hours), but not in two places in
the same moment in time. In this case, the alleged contradiction has disappeared.
Indeed, this car won't even be in Lubbock and not in it at, say, 08:01,
even while it is moving -- since it will be in Lubbock for several minutes
(until it reaches the city boundary). So, in this instance, the car isn't in one place
and not in it in this sub-section of the interval. If that is so, only a very
short-sighted DM-fan will want to take advantage of this escape route (no pun
intended) -- i.e, referring to temporal intervals as opposed to 'moments in
time'. This is probably why Engels didn't refer to temporal intervals, and,
as far as can be ascertained, no DM-theorist has done so since.

8) On a different tack, it is worth asking the
following question: Do these 'contradictions' increase in number, or stay the
same, if an object speeds up? [This is a problem that exercised Leibniz -- see
below.] Or, are the two locations depicted by Engels (i.e., the "here" and the
"not here") just further apart? That is, are the two points that moving body,
B, occupies at the same moment, if it accelerates, just further
apart? But, if it occupies them at the same time, it can't have
accelerated. That is because it hasn't moved from the first to the
second in less time, since it is in both at once. Speeding up, of course,
involves covering the same distance in less time, but that isn't allowed here,
nor is it even possible. In which case, it isn't easy to see how, in a
DM-universe, moving bodies can accelerate if they are in these two locations at
once.

[I am of course using "accelerate" here as it is employed in everyday speech,
not as it is used in Physics or Applied Mathematics. Leibniz argued that if
motion were continuous, it would be impossible to explain faster or
slower speeds. If speed is the number of points a body traverses along its
trajectory in a given unit of time, an increase in speed would involve that body
traversing more points in the same time interval. But, the number of
points in a body's trajectory is infinite; if so, it can't traverse more
points in the same time interval, since, as was supposed in Leibniz's day,
all such infinities are equal (i.e., in modern parlance, they have the same
cardinality).
The only way to account for different speeds, on this view of trajectories
and infinities, is to argue that at a lower speed, a body rests at each
point a bit longer, and vice versa for those that move faster. Leibniz
coupled these observations with the conclusion that motion is in fact illusory!]

Accelerated motion (in the above sense of this word) involves a body being in
(or passing through) more places in a given time interval than had been the case
before it accelerated. But, if B is in these two places at the same
time, how can it pick up speed?

In this Introductory Essay, I have had to
omit much of the material included in Essay Five (Sections
(4)-(7)) that enters into these "fatal defects" in considerable (and technical) detail. I have also had to
outline what I
take to be Hegel's and/or Engels's reasons for asserting that motion is
contradictory, since they themselves manifestly failed to tell us why they
concluded this -- being merely content
to assert it for a fact!

1) It isn't at all easy to ascertain the
'rationale' behind Engels's (and thus Hegel's) conclusion that motion is
contradictory, but it seems to depend on this line-of-argument -- perhaps beginning with a
rejection of the apparent contradiction in E1a, that rejection expressed in E1:

[E1a: An object can be in motion and at rest at
one and the same time.]

E1: An object cannot be in motion and at rest at one and the
same time.

E2: If an object is located at a point it must be at rest at
that point.

E3: Hence, a moving body cannot be located
at a point, otherwise it wouldn't be moving, it would be at rest.

E4: Consequently, given E1, a moving body must both occupy
and not occupy a point at one and the same instant.

But, if this is Engels's (or even
Hegel's) rationale, then he/they offered their readers no reason why we should prefer one
contradiction (E4) over another (E1a). And yet, E1a is a familiar truth, for it
is possible for an object to be at rest with respect to one frame of
reference and yet be in motion with respect to another (that is, that it can be
at rest and in motion at the same time).

On this, Robert Mills had this
comment to make (about Einstein's "Principle of Equivalence"):

"Another way of stating the
principle of
equivalence, a way that better reflects its name, is to say that all
reference frames, including accelerated reference frames, are equivalent, that
the laws of Physics take the same form in any reference frame…. And it is
also correct to say that the Copernican view (with the sun at the centre) and
the Ptolemaic view (with the earth at the centre) are equally valid and equally
consistent!" [Mills (1994), pp.182-83. Spelling altered to conform to UK
English. More on this
here.]

This means that in one frame the Earth would be
stationary, in another it would be moving. In that case, if E1a is true, E4 cannot follow
from E1,
and the imputed rationale behind Engels's 'contradiction' disappears.

E1a: An object can be in motion and at rest at
one and the same time.

E1: An object cannot be in motion and at rest at one and the
same time.

E4: Consequently, given E1, a moving body must both occupy
and not occupy a point at one and the same instant.

2) As noted earlier, Engels's conclusion clearly depends on an
object moving between locations with time having advanced not one instant;
that is, his conclusion implies that the supposed change of place must occur outside
of time
-- or, worse, that it happens
independently of the passage of time --, which is incomprehensible, as
even Trotsky would have admitted:

"How should we really
conceive the word 'moment'? If it is an infinitesimal interval of time, then a
pound of sugar is subjected during the course of that 'moment' to inevitable
changes. Or is the 'moment' a purely mathematical abstraction, that is, a zero
of time? But everything exists in time; and existence itself is an uninterrupted
process of transformation; time is consequently a fundamental element of
existence. Thus the axiom 'A' is equal to 'A' signifies that a thing is equal to
itself if it does not change, that is if it does not exist." [Trotsky
(1971), pp.63-64.]

And yet, how else are we to understand
Engels's claim that a moving body is actually in two places at once? If
that were the case, a
moving object would be in one place at one instant, and it would move to another
place with no time having lapsed; such motion would thus take place outside
of time. But, according to Trotsky, that sort of motion wouldn't exist, for
it wouldn't have taken place in time.

Furthermore, it would mean that while we may
divide location as finely as we wish -- so that no matter to what extent the
spatial aspects of a body's position were partitioned, we would always be able
to distinguish two contiguous points allowing us to say that a moving body was
in those two places at once --, while we can do that with location, we
can't do the
same with respect to time.

Engels's 'argument' thus depends on the claim
that while the location of a particular body is subject to infinite divisibility
(an assumption which, one presumes, is necessary to support the claim that
moving bodies must be in two placesat the same time, no matter how
microscopically close together they are -- which in turn implies that spatial
locations can be given in endlessly finer-grained detail) -- the time interval
during which this takes place isn't subject
to similar division.
Now, this is an a priori
and non-symmetric restriction -- that is, it is applied to time, but not to space.
This is impossible to
justify on either empirical or logical grounds.

[Not one single DM-fan, as far as I am aware, has ever even so
much as tried
to justify this one-sided implied division. In fact, it is clear that not
one single DM-fan even seems to be aware of it!]

If this one-sided constraint is rejected (as surely it
must!), it would mean that no
matter how close together the two locations occupied by a given (moving) object actually
are, we can always specify a finite
timeinterval during which the said movement occurs. That done, the alleged 'contradiction' vanishes. [As
we saw earlier, few would regard it as in any way contradictory that a moving object
can be in two locations during a finite temporal interval.]

Again, the only way to neutralise this
response would be to
counter-claim that a body must be motionless if it is in a certain place at a
certain time (as we saw would be the case if E2 were true). That being so,
it could be argued that if an object is moving, it
must be in two places at the
same time.

E2: If an object is located at a point it must be at rest at
that point.

But, that just repeats the non-symmetrical
restriction noted above (along with its suspect derivation, upon which doubt
was cast earlier). If we can slice up places as finely as we please, so that it is possible to say an
object is in two of them while the 'instant' during which this occurs remains the same, then
we can surely do likewise with respect to time, specifying two times for each of these two
places -- or, at least, specify a temporal interval in which such a change of place
occurs. Again, the only way this response may be blocked would be to argue that while
place is infinitely divisible, time isn't. And how might that be
justified?

Once more, none of this is the least bit surprising since
Engels's claims about motion and change date back to the a priori
speculations of that ancient mystic
Heraclitus
-- a thinker who didn't even
bother to base his wild ideas on anything remotely like evidence (having derived
his 'profound' conclusions about all of reality for all of time from what he
thought was true about the possibility of stepping into a certain river!)
--, and to an Idealist conundrum invented by Zeno. [On Heraclitus's
confusions, see
here.]

[Of course, these observations dispose of the
DM-dogma that contradictions between space and time are only to be expected
since reality is 'fundamentally contradictory'. That is because this
'contradiction' obviously results from a lop-sided convention that
interprets one of these (place) as continuous (and hence subject to infinite
division) and the other (time) as discrete (and hence not so subject).
However, if they are treatedin the same way (as either both continuous
or both discrete), there is no
contradiction. These are, of course, very crude distinctions, but the lack of
clarity here is a direct result of having to make sense of Hegel and Engels's
own terminal lack of clarity on this issue.]

3) Engels also failed to notice that several other
(even more) paradoxical consequences follow from his ideas. One of these is that if a
moving body is anywhere, it must be everywhere, all at once.

The reason for saying this is as follows:
Engels's argument depends on the idea that moving body, B, must be
in two places at the same time -- i.e., in, say, P1andP2
--, otherwise it would be stationary. This allows him to derive a
'contradiction': a moving body must be in two places at once, and it must both be in and
not in at least one of these at the same moment.

But, clearly, if B is in P2
it must also be in P3
in the same instant. If this implication is denied, then the conclusion that a moving body
must be in one place and not in it at the same instant, and in another place at the same
time, will have to be abandoned. If B is in P2
then, unless it is also in P3
at the same time, it must be at rest at that time. This follows from E2:

E2: If an object is located at a point it must be at rest at
that point.

No moving body can be located only at a point
like P2,
it has to be elsewhere at the same time.

So, if it is still true that at
one and the same
instant a moving body is in one place and not in it, and that it is in another
place at the same time (otherwise it would be
stationary), then B must be in P3in the same instant that it is inP2
--
or it wouldn't be moving while at P2,
but would be stationary at P2.

In that case, such a body must be in at least
three places at once: P1, P2,
andP3.

But, the same argument
applies to P3,
so B must also be in P4,
at the same time, and then in P5...,
and so on.

Hence, assuming that B is still moving while at
P2, by the application of a sufficiently powerful
induction,
it can be shown
that any moving body must be everywhere if it is anywhere, all at the same
instant!

[More on this,
here, where
the above argument is presented in greater detail and where several obvious objections
have been rebutted.]

(4) Even odder is the following unrecognised,
absurd consequence of Engels a priori 'argument' (briefly mentioned
earlier):

E5: If Engels were correct (in his characterisation of motion and change), we
would have no right to say that a moving body was in the first of these
'Engelsian locations' before it was in the second.

That follows from L1:

L1: Motion involves a body being in one place and in another place at the
same time, and being in one and the same place and not in it.

As noted earlier, that is because, according to Engels, such a body is in
both places at once. Now, if the above conclusion is valid (that is, if
dialectical objects are anywhere in their trajectories, they are everywhere
all at once), then it follows that no moving body can be said to be anywhere
before it is anywhere else in its entire journey! Again, that is because
such bodies are everywhere all at once. If so, they can't be anywhere first
and then later somewhere else. In the dialectical universe, therefore,
when it comes to motion and change, there is no before and no after!

In that case, according to this 'scientific theory', concerning the entire
trajectory of a body's motion, it would be impossible to say it was at the
beginning of its journey before it was at the end! In fact, it would
be at the end of its journey at the very same time as it sets off!

So, while you might foolishly think, for example,
that you have to board an aeroplane (in order to go on your holidays) before
you disembark at your destination, this 'path-breaking', super-duper theory
tells us you are sadly mistaken: you not only must get on the plane at the
very same time as you get off it at the 'end', appearances to the contrary
notwithstanding, you actually do!

And the same applies to the 'Big Bang'. While benighted non-dialecticians might
think that this event took place billions of years ago, they are surely mistaken
if this 'super-scientific' theory is correct. That is because any two events in
the entire history of the universe must have taken place at the same instant, by
the above argument. Naturally, this means that while you, dear reader, are
reading this, the 'Big Bang' is just taking place!

If, indeed, these are genuine implications of Dialectical 'Logic', then there
can be no "during" and no "while", either, since, as we have seen, this
'path-breaking' theory means that there is no such thing as 'before' and 'after'
when it comes to motion. Hence, if there is no before or after, there can't be a
during or a while. So, even though you might think you have to
wait an hour for a bus, for instance, this 'theory' tells you that this
appearance is illusory. In 'essence' you have been waiting no time at all
-- the bus arrived at your stop in the exact same moment it left the depot!
After all, this 'theory' also tells us that appearances 'contradict' underlying
'essence'; so, dear reader, it might have 'appeared' to you that it took several
minutes to read this Summary, in 'essence', it took no time at all!

To be sure, this is absurd, but that's Diabolical Logic for you once
more!

We saw earlier that Engels's use of
"contradiction" fails to distinguish moving from stationary objects. In that case,
the alleged 'contradiction' he 'derived' is more a function of ambiguities in
the language he used than it is a reflection of objects and processes
in reality.

In Essay Five,
here and
here, I list
numerous examples of similar ambiguities, each of which seems to imply a 'contradiction'
(and all of which Zeno and Engels failed to notice) if we insist on treating language in
this crude and
Philistine way (that is, if we emulate Zeno, Heraclitus, Hegel and Engels, and
ignore such ambiguities).

Now, these ambiguities are relatively easy to
resolve; if the same tactic is applied to the language that the above Idealists
employed, the same result emerges: these 'contradictions' soon vanish.

[I have omitted the details from this summary
for reasons outlined in the Preface, so
the reader is directed to Essay Five for more on this. Follow the two links
above.]

Yet More A Priori,
Dogmatic 'Super-science' From Engels

As noted earlier, Engels performed no experiments (designed to show his ideas
about motion were correct) before or
after he 'derived' his conclusion about motion, and, as far as we know, no dialectician since
has performed any, either. In fact, it is impossible even to imagine or describe
a single observation or experiment that
could conceivably confirm Engels's claims. This is partly because the
'contradictions' to which he alluded can't be observed,
and partly because of the
modal, universal and
omni-temporal character of the
conclusions themselves. That is, no experiment could confirm that every moving
body in the entire universe, for all of time, has to move as Hegel or
Engels say they must.

This means that the only substantiation Engels could have
offered, and did offer, in support of his claims was based on his use of
language. Indeed, had anyone questioned these conclusions his only
response would have involved him reminding sceptics what the words he used really meant.
It would be no good advising non-believers to look harder at the phenomena,
refine their search, or redo some experiment --, which is, of course, why one finds no
experimentalevidence at all in books on dialectics that confirms, or even so much as vaguely supports,
a belief in the
contradictory nature of motion. All we find in its place are dogmatic
assertions based on a brief consideration of a few ambiguous words. [Readers are, of
course, invited to check any randomly-chosen book or article on DM to see if
this allegation is itself correct. They will find it is!]

Thus, Engels's only 'evidence' would have been (indeed, was) based on an appeal to linguistic usage
-- and, even then, it was based solely on Zeno's or Hegel's use of certain words! This
predicament, which Engels shares with all other metaphysicians, invariably
passes off unnoticed because (i) This approach to a priori 'knowledge' is
de rigueur in Traditional Thought, (ii)
It has been going on
for over two millennia, and (iii) It is imagined that by
examining the meaning of words the Armchair
Philosopher is actually studying the world itself, and not simply
inspecting the supposed meaning of a few
specially-selected, and unrepresentative expressions. [We saw this in
Essay Two. See also, Essay Twelve
Part One.]

This is a hallmark of traditional, ruling-class thought: derive
fundamental truths about 'reality', valid for all of space and time, from the
supposed meaning of a handful of words, and then
impose these 'truths' on nature, dogmatically.

True to form, and consistent with the traditional view of
philosophy he had been socialised to accept (as a result of his education in
bourgeois society): Engels
restricted his comments neither (a) to examples of motion he had personally
investigated nor (b) to the entire body of examples witnessed by humanity
since records began.
Despite this, he still felt confident that he could extrapolate from his own understanding of a
few ordinary-looking words to conclusions applicable to every conceivableexample of motion anywhere in the universefor all of time:

"Never anywhere has there been matter
without motion, nor can there be…. Matter without motion is just as
inconceivable as motion without matter. Motion is therefore as uncreatable
and indestructible as matter itself…." [Engels (1976), p.74. Bold emphases
added.]

In fact, what Engels actually did -- and this is the extent of the 'careful' scientific
research he carried out in this area -- all he did was copy the
obscure 'analysis' of
motion he found in Hegel's Logic, an analysis which, as we saw in
Essay Five, was defective anyway.

As we shall also see (in Essays Nine Part
One and
Two, and Twelve (summary
here)), this fact alone has revealing
ideological implications.

"A consistent materialism cannot proceed from
principles which are validated by appeal to abstract reason, intuition,
self-evidence or some other subjective or purely theoretical source. Idealisms
may do this. But the materialist philosophy has to be based upon evidence taken
from objective material sources and verified by demonstration in practice...."
[Novack (1965), p.17. Bold emphasis added.]

This brands Engels's work (in this area), Idealist
-- which shouldn't surprise us given its origin in Hegelian, and Ancient Greek,
Mysticism. Upside down or 'the right way up', Engels's conclusions are
clearly (and solely) based
on an "appeal to
abstract reason, intuition, self-evidence or some other subjective or purely
theoretical source...", and should be rejected as a result.